XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,056,512

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/5/2017, 9:48:53 AM Β· Difficulty 10.8217 Β· 4,788,879 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
a02eb065b216a12a96512f23ba2b18b310655d6d2fc3940eddb0cce5083f96c3
View on Chainz β†—

Height

#2,056,512

Difficulty

10.821657

Transactions

1

Size

198 B

Version

2

Bits

0ad2581c

Nonce

767,245,906

Timestamp

4/5/2017, 9:48:53 AM

Confirmations

4,788,879

Mined by

⛏️ P2SHAMdgprQaozz4RHrW1QQGg6dCEmF8uBjR8h

Merkle Root

04826b7a20ea0cb06fd98864044c8efc903b7410ff694a6f40c8fe8b31a4a837
Transactions (1)
Coinbase04826b7a20ea0c…c8fe8b31a4a837
1 in β†’ 1 out8.5300 XPM109 B
AMdgprQa…F8uBjR8h
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.407 Γ— 10⁹²(93-digit number)
24072671493275792617…64315589472949220799
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
2.407 Γ— 10⁹²(93-digit number)
24072671493275792617…64315589472949220799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.814 Γ— 10⁹²(93-digit number)
48145342986551585234…28631178945898441599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.629 Γ— 10⁹²(93-digit number)
96290685973103170468…57262357891796883199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.925 Γ— 10⁹³(94-digit number)
19258137194620634093…14524715783593766399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.851 Γ— 10⁹³(94-digit number)
38516274389241268187…29049431567187532799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.703 Γ— 10⁹³(94-digit number)
77032548778482536375…58098863134375065599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.540 Γ— 10⁹⁴(95-digit number)
15406509755696507275…16197726268750131199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.081 Γ— 10⁹⁴(95-digit number)
30813019511393014550…32395452537500262399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.162 Γ— 10⁹⁴(95-digit number)
61626039022786029100…64790905075000524799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.232 Γ— 10⁹⁡(96-digit number)
12325207804557205820…29581810150001049599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:58,007,574 XPMΒ·at block #6,845,390 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy